This invention relates to a leading edge construction for reducing drag on an air foil.
The net propulsive force available for aircraft operating at hypersonic speeds imposes severe constraints on their design. The propulsive force required to maintain a constant velocity must equal the vehicle drag, and thus drag reduction is a constant consideration in aircraft design. It is well known that drag can be reduced by reducing the radius of the leading edge. However, it is equally well known that a reduction in the radius of the leading edge increases the amount of heat generated per unit area on the leading edge. For any given operating condition, as the radius of the leading edge decreases, the adiabatic recovery temperature of the leading edge increases, and thus the reduction of the radius of the leading edge has been limited by the thermal properties of the material from which the leading edge is constructed. The minimum size of the radius of the leading edge has been limited by the allowable design temperatures for the available materials.
FIG. 1 is a graph showing the total temperatures experienced in typical flight profiles for high speed vehicles, with air speed (in 1000 feet/sec) on the horizontal axis and altitude (in 1000 feet) on the vertical axis. The isothermal curves are non-linear because of real gas effects such as dissociation and ionization. Five points corresponding to flight conditions of interest for hypersonic aircraft are shown in FIG. 1.
The convective heating rate at a stagnation point on an air foil is dependent on velocity, altitude, and the radius of the surface. FIG. 2 is a graph showing the stagnation point heating on a sphere, with altitude (in 1000 feet) on the horizontal axis, and heating rate divided by the square root of the radius at the stagnation point on the vertical axis. There are separate curves for various velocities (in 1000 feet/second). As shown in FIG. 2, the expected heating rate increases with increasing velocity at constant altitude because of the increased energy level of the impinging molecules. As also shown in FIG. 2, the expected heating rate decreases with increasing altitude at constant velocity because of the reduction in atmospheric density. Five points corresponding to the five points shown in FIG. 1 are also shown on FIG. 2. From FIG. 2 it can be seen that the highest heating rate for the five selected points occurs at an altitude of 150,000 feet, and a velocity of 16,000 feet/second.
Analyses have been performed for each of the five selected points to evaluate expected wall temperatures on the leading edge of hypersonic surfaces. These analyses are graphically displayed in FIGS. 3-7. In each of these figures, the radius (in inches) is represented on the horizontal axis, and temperature (in .degree.R) is represented on the vertical axis. Leading edges with cylindrical shapes at 0.degree., 30.degree., and 60.degree., sweep angles are shown. The curve for a sphere (dashed lines) is also shown for reference. These curves confirm that the maximum temperature for the five selected points occurs at an altitude of 150,000 feet, and a velocity of 16,000 feet/second. The temperature graphs of FIGS. 3-7 represent radiation equilibrium values, i.e. they assume that all aeroheat generated is dissipated only by radiation (assuming a surface emissivity of 0.9).
With currently available materials, the maximum allowable temperature for air foil components is no more than about 5000.degree. R. As shown in FIG. 5, at an altitude of 150,000 feet, and a velocity of 16,000 feet/second, this translates into a minimum leading edge radius of about 0.2 inches over a 60.degree. sweep. Any further reduction in the radius to reduce drag under these operating conditions would result in excessive surface temperatures. Thus, unless some cooling means are provided, the leading edge radius for likely hypersonic flight profiles is unduly limited.
The benefits of increasing the sharpness of the leading edge is shown in FIG. 8, in which the fractional change in leading edge radius is represented on the horizontal axis, and drag (in pounds) is represented on the vertical axis. The FIG. 8 graph is based on calculations for an aircraft having a weight of 1200 pounds, a lift/drag (L/D) ratio of 3.5, and a 10.degree. taper angle. Operation at an altitude of 150,000 feet, and a velocity of 16,000 feet/second was assumed. The FIG. 8 graph indicates that, as would be expected, the reduction in drag is a function of the original radius. Thus, the larger the original radius, the larger the potential reduction in drag. From FIG. 8, it can be seen that the 0.2 inch leading edge radius discussed above (which operated at the 5000.degree. R temperature limit) experiences a drag of about 343 pounds. However, the drag approaches about 270 pounds as this radius is reduced toward 0.
The effect of reducing the leading edge radius on the L/D ratio is shown in FIG. 9, in which the change in leading edge radius is represented on the horizontal axis. The FIG. 9 graph was prepared under the same assumptions and conditions as the FIG. 8 graph. The 0.2 inch leading edge radius discussed above, of course, has an initial L/D ratio of 3.5. However, the L/D ratio approaches 4.44 as the leading edge radius is reduced toward 0, indicating that significant improvements in performance are available if the leading edge radius could be reduced beyond the limit imposed by maximum temperature considerations.
The effect of reducing the leading edge radius on the L/D ratio under other operating conditions has also been studied. FIG. 10 is a graph of the change in leading edge radius versus L/D ratio at an altitude of 150,000 feet and a velocity of 6,000 feet/second. FIG. 11 is a graph of the change in leading-edge radius versus L/D ratio at an altitude of 100,000 feet and a velocity of 6,000 feet/second. The FIGS. 10 and 11 graphs illustrate that improvements in performance are available for reductions in leading edge radius under these conditions as well.